Measuring device.



No. 745,257. PATENTED Nov; 24, 1903.

P. M. STEADMAN.

MEASURING DEVICE.

APPLIOATIOK FILED SEPT. 28, 1901.

N0 MODEL.

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iio. 745,257.

UNrrnD STATES IPatented November 24, 1903.

PATENT OFFICE.

FRANK M. STEADMAN, OF PUEBLA, MEXICO, ASSIGNOR OF ONE-HALF TO GUS E.TRAGER, OF PUEBLA, MEXICO.

MEASURING DEVICE.

SPECIFICATION forming part of Letters Patent No. 745,257, dated November24, 1903. Application filed September 28, 1901. Serial No. 76.878. (Nomodel.)

To all whom it may concern:

Be it known that I, FRANK M. STEADMAN, a citizen of the United States ofAmerica, and a resident of Puebla, in the State of Puebla and Republicof Mexico, have inventeda new and Improved Measuring Device, of whichthe following is a full, clear, and exact description.

The object of the invention is to provide a new and improved measuringdevice more especially designed for measuring surfaces or openings in avery. quick and convenient manner and without requiring mechanicalcalculations.

The invention consists of novel features and parts and combinations ofthe same, as will be fully described hereinafter and then pointed out inthe claims.

A practical embodiment of the invention is represented in theaccompanying drawings,

3 forming a part of this specification, in which similar characters ofreference indicate corresponding; parts in all the views.

' Figure 1 is a perspective view of the improvement as applied. Fig. 2is an enlarged face view of the improvement. Fig. 3 is a side elevationof the same. Fig. 4 is a rear sectional elevation of the tape-casing;and Figs. 5 and 6 are top and bottom views of the tape used in thedevice, the tape for convenience being shown in each view as separatedinto two sections.

The improved measuring device consists, essentially, of a surface-planepreferably in the form of a disk A, on which is secured a tape-casing B,in which winds and unwinds a tape O,provided at its outer end with asuitable handle D, adapted to be taken hold of by the operator to drawthe tape out of the casing or to allow the tape to wind up in thecasing, as indicated in Fig. 4. A suitable locking and releasing deviceE is provided on the casin g B and is under the control of the operatorto stopand lock the tape 0 in position after the same has been drawn outof the casing a desired distance, as hereinafter more fullyexplained,the said device when released allowing the tape to rewind inthe casing in the usual manner. As this part of the device may be of anywell-known construction further description thereof is not deemed necessary. The casingB and its tape 0 are so arranged relative to the disk Athat when the tape 0 is drawn out it extends approximately centrally tothe disk A and at right angles thereto, as will be readily understood byreference to the drawings. The tape 0 is provided on its upper and lowerfaces with graduations O and 0 respectively, (see Figs. and 6,) .ofwhich the graduation O is used in connection with the surface-plane ordisk A and the bottom graduation O is used in connection with anaperture A, formed in the surface-plane or disk A, the said aperture Aserving for viewing small objects the surface of which is to be measuredby the device. It is understood that the diameter of the disk-A isprcdeterminedsay ten centimetersand the aperture A has alikcwisepredetermined diameter say five millimetersand the graduationsO C havevaluescorrespondin g to the predetermined diameters of the disk and theaperture. The tape 0 is also provided with a line or point e, from whichthe measurement is made.

The opening A because of its being onetwentieth of the diameter of thedisk A will make the same measure of any surface with one-twentieth thelength of tape as would be made with the disk A, using twenty times thelength of tape. Thus by the use of the small opening A, I avoid thenecessity of a very long tape that could not be handled by one personalone.

Thetheoryofmeasurementinvolvedisasfollows: The point c on the tape isalways the center from which the measurement is made. A hollow sphere orglobe of any size, with the eye of the observer supposed to be at thecenter,would shut off from the observer everything in every directionoutside of the sphere.

As a circle is a line that bounds and measures the directions outwardfrom or in toward a center point on a plane surface so a sphere or globeis a surface which bounds and measures all the directions outwardfrom'or in toward a center point not only along a plane, as does thecircle, but in every possible direction. If lines be ICC named sphere asdid the corresponding area of the said portion of the first-named sphereto its entire area. Consequently if lines be drawn from each element ofthe periphery of any plane surface to a point outside the surface andopposite the center thereof these lines will cut from all spheresconcentric with said point areas which in each case will bear the sameconstant ratio to the entire area of the sphere to which said areabelongs. This is true no matter how far into space the concentricspheres may be supposed to extend. The whole sky may be regarded as sucha surrounding surface and the visible expanse of sky as the half of sucha surrounding sphere or globe. Any circle of fixed size-say a fine wirecircle of ten centimeters in diameter-placed on the surface of any globe(whose diameter is not less than that of the circle) will inclose acertain area, which will be in any case some exact fractional part ofthe whole area of that globe. The larger the globe the less would be thefractional part of its whole surface that would be outlined by orinclosed in the circle when placed against it. To ascertain thedimensions of a globe upon whose surface such a circle would inclose anexact predetermined part of the whole area, as one-fourth or onesixty-fourth, is simply a mathematical problem.

Based on the above truths the measurement is made as follows:

First. The surface of a sphere or globe is divided into one hundred andtwenty-eight parts called units, each unit into one hundred andtwenty-eightparts called B units, each B unit into one hundred andtwentyeight parts called 0 units.

Second. The diameter of the circular spheresection, which is to be themeasure of exact fractional parts of the sphere-surface, is for reasonsof convenience chosen to be ten centimeters, which is the diameter ofthe circle of such a section measured across the flat side of thatsection after it is supposed to be cut off from the sphere. The flatside of such a sphere-section is what is represented, respectively, bythe disk A and the small opening A in the measuring device. The diskwhen viewed from a given point, as the center c, subtends a certaindefinite portion of the area of a sphere concentric with the said point,

and the graduation O on the tape expresses this ratio for particularpositions of the disk, while the graduation C expresses this ratio forthe opening A in the disk.

Third. The sizes of the different spheres or globes in which thecircular section of constant diameter will occupy thirty-two,sixteen,eight, four, two, one, and the intermediates twenty-four, twelve, six,three, one and onehalf units, or one hundred and twenty eighths of thesphere-surface, were found by mathematical calculation; also, the sizesof the spheres in whichthe constant disk of ten centimeters will occupysixty-four, thirty-two, and sixteen B units or one hundred and twentyeighths of a unit of the sphere-surface; also, the sizes of the spheresin which the smaller constant disk or opening of five millimeters willmeasure eight, four, two, one B units or one hundred and twenty eighthsof a unit, and sixty-four, thirty-two, sixteen, and eight 0 units of thesphere-surface, or one hundred and twenty eighths of a B unit. The diskA and small opening A are always in theory supposed to be a part of theentire spheresurface, just as in speaking of a certain number of degreeswe know that in theory the degrees are parts of complete circles andthat whether those circles reach to the stars or are only outlined on asmall piece of paper in front of our eyes there is no difference in thethought of degrees that is involved, as it is a relative and not anabsolute measurement. So it is in measuring with the device. When thedisk A of ten centimeters occupies thirty-two one hundred and twentyeighths of a whole sphere-surface, large or small, in relation to itscenter point, the disk is only M0289 from that center-point, which is eon the tape. As thirty-two one hundred and twenty eighths is equal toone-fourth of the entire sphere-surface it is very plain that the diskmust be very close to the center point in order .to occupy so much ofthe sphere-surface. Now when the disk 0ccupies only two one hundred andtwenty eighths of the sphere-surface or one sixtyfourth of that surfaceit is evident that it cannot be so close to the center-point ofmeasurement, or c. WVe find, in fact, by working out the problem thatthe disk must be just M. 1953 from c. As the disk recedes from c itoccupies less and less of the sphere-surface, just as two points a fixeddistance apart occupy less degrees around a point of measurement themore they are removed from that point. The disk A at M.2795 from coccupies one unit or one one hundred and twenty eighth of thesphere-surface. The diskA at M3977 from c occupies one-half unit ofsphere surface. At M.7 988 from c the diskAoccupies one-eighth of a unitof spheresurface or sixteen B units of it. N ow as M.'7988 is about asfar as an arm can conveniently reach to hold the disk the size of themeasure is at this point changed to M.0O5 in diameter, the small openingA, and on the under side of the tape the same center 0 is located, andthe small opening A at M0565 from coccupies one-sixteenth of a unit ofsphere-surface or eight-B units of it, and the farther it retires from.c the less sphere- .surface it occupies around 0, which is the center ofmeasurement. At M.l6 from c it occupies only one one hundred and twentyeighth of one one hundred and twenty eighth of the sphere-surface or one1-3 unit of it. At M6406 from C it occupies only eight one hundred andtwenty eighths of one one hundred and twenty eighth of one one hundredand twentyeighth of the sphere-surface or eight 0 units of it. This isless space than is occupied by the surface of the sun in the heavens,and is, I think, as small a measurement as is necessary to make in theactual use of the meter. Thescientists or mathematicians may laterreduce the subdivisions to any degree of fineness that they may finddesirable.

Fourth. The tape-lengths from c or the center to the differentunit-numerals on the tape where the disk is to be placed is in the caseof each particular unit value or numeral the perpendicular of a triangleof which the radius of the corresponding sphere or globe is thehypotenuse and one-half of the disk diameter is the base, the same diskdiameter being used in the calculation that was used in calculating thesphere whose radius is the hypotenuse in each calculation.

In using the device for ascertaining the point from whichany surfaceshalLbe viewed in order that it shall occupy a predetermined number ofunitsas, for example, the position of the eyes with reference to theclock-face F, as indicated in Fig. 1the tape is pulled out until themark at the numeral representing the units desired is even with the diskA, and then the locking device E is actuated to hold the tape in place.The operator then raises the disk in the left hand and, keeping the tapestretched, places the letter 0 just below the eye with the right hand,as shown in Fig. 1. In this position the disk measures the chosen numberof units in relation to the mark at the letter c or the eye in practice,and to find the point from which the clockface F will measure the samethe operator must walk toward or from the clock-face until it is seen tocoincide with the periphery of the disk A. Then from that point ordistance from the clock-face F it is found that it occupies the samenumber of units as is indicated by the numeral which is placed even withthe disk A. in this position the clock-face F measures one unit or oneone hundred and twenty eighth of a sphere-surface in its relation to theeye of the observer. WVhatever be the number of units it is desired thata chosen surface shall occupy that numeral is placed even with the diskA, and the-point in front of that surface from which it will measurethat number of units is found in the same manner, as previouslydescribed. For example, suppose it is desired to find that point fromwhich the clock-face F will measure thirty-two B units or thirty-two onehundred and twenty eighths of one one hundred and twenty eighth of theentire sphere-surface. The line at the numeral 32 B is placed even withthe disk, and with the tape and disk in position, as before explained,the operator walks away until the clock-face F and the disk A coincide.It will now be known that the clock-face F occupies from the pointoccupied by the eye of the operator and in relation to that point thedesired thirty-two one hundred and twenty eighths of one one (See Fig.1.) With the meterhundred and twenty eighth of the entire sphere-surfaceor, as explained, thirty-two B units.

When it is desired to measure objects smaller than the disk or largeobjects at a distance where they are hidden by the disk at 16 B, thenthe numbers on the under side of the tape (see Fig. 6) must be placedeven with the disk and the measuring done through the aperture A.

It will be seen that by theme of the device two kinds of measurement canbe hadnamely, the number of units being predetermined, the problem is tofind the point from which the measured surface will measure the desirednumber of such units, and the other,

the point of view being predetermined, to find the number of units thesurface occupies when viewed from that point.

To measure from a chosen point the value A forward or backward until itsrim coincides as nearly as possible with the outlines of the surface tobe measured. If the outer rim of the disk cannot be made small enough tomeasure it, then use is made of the aperture A, as above explained. Inusing the small aperture A it is easier to place it close to the eyefirst and then to move the disk away until the desired point is reached,as the surface to be measured is always in sight through the aperture:When the disk A, however, is used, it is easier to move it far away atfirst and gradually draw it up until its rim coincides with the surfaceto be measured, as the surface may be plainly visible while the meter isadjusted relative to the surface. When the measurement is made, the tapenumber nearest the disk indicates the value of the surface. It isexpresslyunderstood that if the rim of the disk A is used the numbers ofthe graduations on top of the tape 0 are used but when the aperture A isICO employed then the numbers on the under side of the tape 0 are used.

In order to prove the usefulness ofthe device as a measurer of a spacethrough which light is allowed to pass, I proceed as follows: A chair isplaced a few steps from a window through which the sky may be seen, andthen the measure of the window is taken by the to number 3 and thenplaces the chair nearer to the window until the window-open-.

in-g coincides as nearly as possible with the rim of the disk. When thishas been done,

Suppose it is desired that.

the window-opening will have a value of three units. Thus by the use ofthe device the object to be illuminated by the rays of light enteringthe window can be at once placed in the proper position, so that thedesired amount of light passes upon the object, irrespective of the sizeof the window.

As the circle always has the same value in degrees no matter what itsabsolute size may be, so I have divided the sphere into parts or unitshaving the same value whatever the size of the sphere. A line drawn fromhorizon to horizon up through the zenith measures the half of a boundingcircle which we call one hundred and eighty degrees. So the visible skyas a surrounding surface or expanse we may say measures sixty-foursphere units, just as the half-circle measures one hundred and eightydegrees. As this fact in relation to the sphere or globe does not appearto have been heretofore recognized by scientists, I have been obliged tomake such division of the sphere-surface and to establish the unit andscale of measurement as I have thought would be the most practical.

The number (128) was chosen as the number of parts into which thesphere-surface should be divided for convenience only, because such adivision seemed to answer best in the use of the measurement itself. Forinstance, in the practical use of the measure in measuring a visibleexpanse of skyas seen through a window-opening the amount that should beused in taking a portrait by photography is from three to six units ofthat sky. It is seen that these are convenient numbers and that by thechosen division into one hundred and twenty-eight parts or units thoseparts are made of convenient value in practice.

A special reason why one hundred and twenty-eight was chosen is becauseit is a number that can be divided continuously by two without resultingin a fraction until after arriving at unity, and then the use offractions is avoided by dividing the unit again into one hundred andtwenty-eight parts or 13 units and the B unit again into one hundred andtwenty-eight parts or C units.

Having thus described my invention, I claim as new and desire to secureby Letters Patent- 1. A measuring device consisting of a tape providedwith a series of graduations and having an extreme graduation c at ornear one end, the said extreme graduation or point forming asphere-center, and a flat circular disk of predetermined diametercorrelating to the values of the graduations on the tape, the said diskbeing arranged to subtend more or less of said sphere-surface, equal,when the disk is at any particular graduation on the tape and at rightangles thereto, to such fractional part of the area of thesphere-surface as is expressed by said graduation, as set forth.

2. A measuring device consisting of a tape provided with a series ofgraduations and having an extreme graduation c at or near one endforming a sphere-center and a disk having a small circular opening ofpredetermined size and correlating to the Values of the graduations onthe tape, the said opening exposing more or less of said sphere-surface,when viewed from the point or graduation forming the sphere-center,equal, when the disk is at right angles to and at any particulargraduation 011 the tape, to such fractional part of the area of thesphere-surface as is expressed by said graduation.

3. A measuring device comprising a disk, a tape-casing secured thereon,and a tape provided with graduations and winding and unwinding in thesaid tape-casing, the tape being arranged to extend approximately fromthe center of said disk and at right angles to the face thereof, wherebywhen the disk is at any particular graduation on the tape the edges ofthe disk may be equidistant from a point 011 said tape representing thecenter from which the measurement is made, as set forth.

4. A measuring device having a disk, and a tape adj ustably connectedwith the disk and working at right angles thereto, said tape havinggraduations, each representing the ratio of that portion of the maximumsurface of a sphere that may be subtended by the disk when viewed fromthe sphere-center and the tape adjusted to said center, to that of theentire sphere, as set forth.

5. A measuring device having a disk formed with an aperture, a tape adjustably connected with the disk and having graduations, eachrepresenting the ratio of that portion of the surface of a sphereexposed through the said aperture in the disk when viewed from thesphere-center and the tape adjusted to said center, to that of theentire sphere, the tape, when in operative position, being at rightangles to the plane of the disk, as set forth.

6. A measuring device having a tape provided with graduations eachrepresenting the ratio of that portion of the maximum sur face of asphere subtended by a disk of predetermined size when viewed from thespherecenter and the tape adjusted to said center, to that of the entiresphere, as set forth.

7. A measuring device having a tape provided with graduations and havinga mark indicating the center from which the measurement is made, and adisk used in connection with the tape, the tape being arranged to extendapproximately from the center of said disk and at right angles to theface thereof, the disk when viewed from the measuring-center on thetape, subtending a definite portion of the area of an imaginary sphereconcentric with said measuring-cen ter, the said graduations on the tapeexpress ing this ratio for particular positions of the disk, as setforth.

8. A measuring device, comprising a disk of predetermined size, havingan aperture also of predetermined size relative to that of IIO and atright angles to the face of said disk,

the said tape being provided with graduations, representing the ratio ofthat portion of the surface of a sphere that may be subtended by thedisk, when viewed from thesphere-center and the tape adjusted to saidcenter, to that of the entire sphere, the tape also having graduationsrepresenting the ratio of that portion of the surface of a sphereexposed through said aperture, to that of the entire sphere, the tapebeing also adjusted to the sphere-center whenthe aperture is employed,as set forth.

9. A measuring device, comprising a disk having a slot formed therein, atape-casing secured in said slot and projecting beyond the faces of thedisk, and a tapewinding and unwinding in the said tape-casing and atright angles to the disk, as set forth.

10. Ameasuring device comprising a disk of predetermined diameter, thesaid disk being provided with an aperture also of predetermined diameterrelative to that of the disk, and a tape having ameasuring-pointthereon, representing the center of an imaginary globe orsphere, the said tape being adjustable at right angles to the said disk,and provided with graduations on one side indicating divisions andsubdivisions of a complete sphere or globe surface and having valuescorresponding to the size of the disk, and graduations on the other sideof said tape indicating subdivisions of a sphere-surface and'havingvalues corresponding to the size of the aperture in the disk, the diskwhen viewed from the measuring-point on the tape subtendin g a definiteportion of the area of the imaginary sphere concentric with said point,the first-mentioned aperture in the disk, as set forth.

11. A measuring device, comprising a disk of predetermined diameter anda tape arranged to extend at right angles to the disk, the said tapebeing provided with graduations indicating divisions and subdivisions ofa complete globe or sphere surface, the graduations having valuescorresponding to the size of the disk, the said tape having a graduationat or near its outer end representing the center of an imaginary globeto be measured, the said disk wh en placed at any particular graduationon the tape subtending more or less of the globe-surface according toits distance from the said extreme graduation, thereby allowing the diskto become at will the measure of a large section of a small globe or agradually smaller section of a larger globe.

12. A nleasuring'device comprising a disk of predetermined diameter, anda tape arranged to extend at right angles to said disk and provided witha graduation representing a sphere-center, and a series of graduations,

having values corresponding to the diameter of the disk, the saidgraduations representing divisions and subdivisions of saidsphere-surface and at which said disk maybe placed to subtend exactfractional parts of the spheresurface, when the disk is viewed from thepoint representing the sphere-center.

18. A measuring device, comprising a tape provided with graduationsforming a scale representing divisions and subdivisions of the totalsurface of a sphere, the said graduation-s comprising unit-graduationseach representing one one hundred and twenty eighth of the total area ofthe sphere-surface, and graduations representing divisions of saidunit-graduations, and a disk of predetermined size used in connectionwith and at right angles to the tape, the graduation of the tape havingvalues corresponding to the size of the disk, the tape having ameasuring-point at or near its end indicating an imaginarysphere-center, the disk when placed at any particular graduation on thetape and viewed from the said measuring-point subtending the exactfractional part of a sphere-surface indicated by said graduation, as setforth.

14. Ameasuringdevice,comprisingadiskof predetermined diameter, the saiddisk being provided with a circular opening also of predetermineddiameter relative to that of the disk, and a tape having a pointindicating the center from which the measurement is made, the said tapebeing provided with a series of graduations forming a scale representingdivisions and subdivisions of a globe-surface, the scale havingunitgraduations each representing one one hundred and twenty eighth ofthe total area of a globe-surface, B unit-graduations each representingone one hundred and twenty eighth of a unit in value and 0unitgraduations each representing one one hundred and twenty eighth of aB unit in value, one face of the said tape being provided with saidgraduations from thirty-two units down to sixteen B units, the saidgraduations, when the tape is extended at right angles to the disk,being used in connection with the disk as the latter is moved to andfrom the point of measurement 0n the tape, the disk, when at anyparticular graduation on the tape, and viewed from the point ofmeasurement, subtending a definite portion of the area of an imaginarysphere concentric with said point of measurement, the said graduation atwhich the disk is placed expressing this ratio, the other face of thetape having graduations from eight B units to eight 0 units and used ina similar manner in connection with the opening in the disk, as setforth.

In testimony whereof I have signed my name to this specification in thepresence of two witnesses.

FRANK M. STEADMAN.

